Answer:
[tex]\frac{1}{72}[/tex]
Step-by-step explanation:
We have been given that there are total 9 people who entered the drawing competition. There are 3 prizes to be distributed to the winners. The total number of ways that 3 prizes can be awarded to the 9 people can be determined as 9*8*7 = 504.
The total number of ways in which I win the first prize and my mom wins the second prize would be 1*1*7 = 7.
Therefore, the probability that I win the first prize and my mom wins the second prize would be: [tex]\frac{7}{504}=\frac{1}{72}[/tex]
Answer:
it’s 7
Step-by-step explanation:
Find the volume of a sphere
v=4/3 πr^3.
Use this formula
It could be possibly this
v=4/3 πr^3
I hope it helped AND I hope it's right,,
The inverse of y = 2x + 2 is
Answer:
The inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].
Step-by-step explanation:
The given function is
[tex]y=2x+2[/tex]
The step and shown below to find the inverse of the function.
Step 1: Interchange x and y.
[tex]x=2y+2[/tex]
Step 2: Isolate variable y.
[tex]x-2=2y[/tex]
[tex]\frac{1}{2}(x-2)=y[/tex]
[tex]\frac{1}{2}(x)+\frac{1}{2}(-2)=y[/tex]
[tex]\frac{1}{2}(x)-1=y[/tex]
Therefore the inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].
Answer:
The inverse of y = 2x+2 is 1/2x-1.
Step-by-step explanation:
Given equation is
y = 2x+2
let y = f(x) = 2x+2
We have to find the inverse of given function.
Adding -2 to both sides of given equation,we get
y-2 = 2x+2-2
y-2 = 2x
dividing by 2 to both sides of above equation , we have
(y-2) / 2 = 2x / 2
y/2 - 1 = x
Swapping equation, we have
x = y/2-1
put x = f⁻¹(y) in above equation ,we have
f⁻¹(y) = y/2 -1
Replace y with x , we have
f⁻¹(x) = x/2-1
Hence , the inverse of given function is 1/2x-1.
A computer is normally $550 but is discounted to $385 which precent of the original price does mark pay
Answer:
70%
Step-by-step explanation:
We assume, that the number 550 is 100% - because it's the output value of the task.
We assume, that x is the value we are looking for.
If 100% equals 550, so we can write it down as 100%=550.
We know, that x% equals 385 of the output value, so we can write it down as x%=385.
Now we have two simple equations:
1) 100%=550
2) x%=385
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=550/385
Now we just have to solve the simple equation, and we will get the solution we are looking for.
Solution for 385 is what percent of 550
100%/x%=550/385
(100/x)*x=(550/385)*x - we multiply both sides of the equation by x
100=1.4285714285714*x - we divide both sides of the equation by (1.4285714285714) to get x
100/1.4285714285714=x
70=x
x=70
PLEASE PLEASE PLEASE HELP! WILL BE GIVING OUT BRAINLIEST AND LOTS OF POINTS!!!!!!!
Gina looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one wall in the plan is 17 inches. The length of the diagonal of the floor of the room in the plan is approximately 18.79 inches. Is the room in the shape of a square? Explain how you determined your answer. Show all your work.
Final answer:
The room is not a square, as shown by applying the Pythagorean theorem, because the calculated diagonal of a square with 17-inch sides would be approximately 24.04 inches, not 18.79 inches.
Explanation:
To determine if the room is in the shape of a square, we can use the Pythagorean theorem, which relates the lengths of the sides of a right-angled triangle. For a square, the lengths of all four sides are equal. Therefore, if we assume that the length and the width of the room are both equal to the given wall length of 17 inches, the diagonal (d) of the square can be calculated using the Pythagorean theorem:
c2 = a2 + b2
where c is the length of the diagonal, and a and b are the lengths of the sides of the square.
So, it would be:
c2 = 172 + 172
= 289 + 289
= 578
Now we find the square root of 578 to find the length of the diagonal (c):
c ≈ √578 ≈ 24.04 inches
Since the given diagonal length is approximately 18.79 inches, and our calculated value for the diagonal of a square with sides 17 inches is approximately 24.04 inches, the room is not a square. The diagonal is too short for the room to be a square given the 17-inch wall.
My teacher never taught us this, but expects us to know
I'll do problem 77 to get you started
Point slope form is this general equation
y - y1 = m(x - x1)
with m as the slope and (x1,y1) as the point the line goes through. In this case, m = -4 and (x1,y1) = (-2,9)
Plug those values into the equation to get...
y - y1 = m(x - x1)
y - 9 = -4(x - (-2))
y - 9 = -4(x + 2) see note 1
y - 9 = -4x - 8
y = -4x - 8 + 9
y = -4x + 1 see note 2
--------
note 1: If your teacher wants the answer in point slope form, then you stop on this line. Otherwise, keep going
note 2: This is in slope intercept form y = mx+b with m = -4 as the slope and b = 1 as the y intercept
-2⁄3 a − 6 = 12
a =
Answer:
a = -27
Step-by-step explanation:
-2⁄3 a − 6 = 12
add 6 to both sides:-
-2/3 a -6 + 6 = 12 + 6
-2/3 a = 18
Now multiply each side by -3/2:-
a = 18 * -3/2 = -54/2
= -27
To solve the equation -2⁄3 a - 6 = 12 for 'a', add 6 to both sides of the equation and then multiply both sides of the equation by -3/2 to isolate the variable 'a'. The value of 'a' that satisfies the equation is a = -27.
Explanation:To solve the equation -2⁄3 a - 6 = 12 for 'a', we can start by isolating the variable on one side of the equation. First, let's add 6 to both sides of the equation:
-2⁄3 a - 6 + 6 = 12 + 6
-2⁄3 a = 18
Next, we can multiply both sides of the equation by -3/2 to get:
(-3/2)(-2/3 a) = (-3/2)(18)
a = -27
The value of 'a' that satisfies the equation -2⁄3 a - 6 = 12 is a = -27.
Simplify 7x +42/ x2+13x +42
[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{x^2+7x+6x+42}=\dfrac{7(x+6)}{x(x+7)+6(x+7)}\\\\=\dfrac{7(x+6)}{(x+7)(x+6)}=\boxed{\dfrac{7}{x+7}}[/tex]
Your answer should be 2(10x^3+21x^2+21) over X^2 2(10x^3+21x^2+21)/X^2 unless the / was a fraction symbol and not a division symbol then your answer would be 7 over x+7 7/x+7
What is the value of the problem below?
Answer:
90
Step-by-step explanation:
The first term = 6* 2^0 = 6
The second term = 6 * 2^ (2-1) = 6*2 = 12
The third term = 6* 2^(3-1) = 6*2^2 = 6*4 = 24
The fourth term = 6* 2^(4-1) = 6* 2^3 = 6*8 = 48
S4 is the sum of the 1st four terms
S4 = 6+ 12+24+ 48 = 90
Which quantity is proportional to 35⁄80? Check all that are true. 3⁄5 14⁄36 26⁄52 21⁄48 7⁄16
Hey there!
"Which quantity is proportional to [tex]\frac{35}{80}[/tex]?"
The easier way, I figured out how to solve this particular problem is simplify the fraction to decimal
[tex]\frac{35}{80}[/tex] [tex]= 0.4375[/tex]
[tex]\frac{3}{5}[/tex] [tex]= 0.60[/tex] so, this one isn't your answer[tex]\frac{14}{36}[/tex][tex]=0.288889[/tex] so this one isn't your answer [tex]\frac{26}{52}[/tex][tex]=0.50[/tex] so this one isn't your answer[tex]\frac{21}{48}[/tex][tex]=[/tex][tex]=0.4375[/tex] this one is your answer [tex]\frac{7}{16}[/tex][tex]= 0.4375[/tex] so this one is your answer[tex]\boxed{Answer: \frac{21}{48} AND \frac{7}{16}}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Answer:
3/5 no
14/36 no
26/52 no
21/48 yes
7/16 yes
Step-by-step explanation:
A function f(x) is graphed.
What is the slope of the function? M= 1,2,3,4
What is the y-intercept of the function? B= -2,-1,1,2
Which equation represents the graph of the function y=-x+2 , y=x+2 , y=2x+1 , y=-2x+1
Answer:
Point-Slope form: The equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex] ......[1]
where m is the slope and [tex](x_1,y_1)[/tex] is the point on the line.
From the given graph:
Consider two points i.e,
[tex](0, 1)[/tex] and (-0.5, 0)
Calculate slope:
Formula for slope is given by;
[tex]\text{Slope}(m) = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values we have;
[tex]m = \frac{0-1}{-0.5-0} = \frac{-1}{-0.5} = \frac{10}{5} =2[/tex]
Now, substitute the value of m = 2 and (0, 1) in equation [1] we have;
[tex]y-1 = 2(x-0)[/tex]
y-1 = 2x
Add 1 to both sides we get;
y = 2x+1
On comparing equation y = 2x+1 with the slope intercept form of a line (i.e, y = mx+b) then we have;
slope(m) = 2
y-intercept(b) = 1
therefore, the slope of the function:
m = 2
y-intercept(b) = 1
and the equation represents the graph: y = 2x+1
Answer:
2
1
y = 2x + 1
Step-by-step explanation:
Compute the amount of interest earned in the following simple interest problem. A deposit of 1,295 at 7% for 180 days=____. (note: use 365 days in a year
The interest earned is approximately $50.06.
To calculate the amount of interest earned in a simple interest problem, we can use the formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{\text{Total days in a year}} \][/tex]
Given:
- Principal (P) = $1,295
- Rate (R) = 7% or 0.07
- Time (T) = 180 days
- Total days in a year = 365 days
Plugging these values into the formula:
[tex]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} \approx 1295 \times 0.07 \times 0.493150685 \]\[ \text{Interest} \approx 50.05958904 \][/tex]
All geometric figures,shapes,and solids can be named using sets of
Answer:
All geometric figures, shapes and solids can be named as a sets of surface regions and plane regions and they all lie in three dimensional spaces.
Step-by-step explanation:
What is the result of factoring out the GCF from the expression (24 + 36)?
A. 12 × (12 + 18)
B. 12 × (2 + 3)
C. 6 × (8 + 12)
D. 12 × (4 + 6)
24 = 2 · 2 · 2 · 3
36 = 2 · 2 · 3 · 3
GCF(24, 36) = 2 · 2 · 3 = 12
24 = 12 · 2
36 = 12 ·3
24 + 36 = 12 × 2 + 12 × 3 = 12 × (2 + 3)
Answer: B.The result of factoring out the Greatest Common Factor (GCF) from the expression (24 + 36) is 12 × (2 + 3).
Explanation:To factor out the Greatest Common Factor (GCF) from the expression (24 + 36), we first need to determine the largest number that divides evenly into both 24 and 36. The GCF of 24 and 36 is 12. We divide each term by the GCF to factor out it from the expression:
24 ÷ 12 = 2
36 ÷ 12 = 3
Thus the expression factored out by the GCF is 12 × (2 + 3).
Learn more about Factoring Out GCF here:https://brainly.com/question/29055991
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Julie had $2000 in her savings account, but then she purchased a plane ticket for spring break, decreasing her savings account by 14%. How much was her plane ticket? How much money was left in the account after she bought it?
Step-by-step explanation:
What is equal to 19.04 divided 5.6
Answer: 19.04 divided by 5.6 is 3.4
Step-by-step explanation:
2. Marco has a jug with 37 ½ ounces or juice. He wants to use some small cups to pass out samples of the juice. Each cup hold 2 ½ ounces of juice. How many cups can marco fill with juice samples?
Answer: Marco can fill 15 of the 2 1/2 Cups
Step-by-step explanation:
37.5 divided by 2.5
or
37 1/2 divided by 2 1/2
Answer:
Marco can fill 15 of the 2 1/2 Cups
37 1/2 divided by 2 1/2
the price of family dinner was $48.00 . A sales tax of 5% to the final bill. The family left a $10.08 tip. If the family included the sales tax when calculating the tip, what percent tip did the family leave?
Answer:
20% tip
Step-by-step explanation:
Dinner: $48.00
Tax: 0.05($48.00) = $2.40
Total (final) bill before tip: $50.40
Tip: $10.08
Percentage tip was then $10.08 (100%) / $50.40 = 20%
The family left a 20% tip.
Solve. Give your answer in scientific notation. (3.4x10^2)x(2x10^3)
A.1.4x10^-1
B.6.8x10^5
C.5.4x10^5
D.6.8x10^6
Plz answer
Final answer:
The multiplication of (3.4x10²) and (2x10³) results in 6.8x10⁵ after multiplying the coefficients and adding the exponents. Therefore, the correct answer is option (B).
Explanation:
Considering, the question it has asked to solve the following arithmetic operation in scientific notation: (3.4x10²)x(2x10³).
To solve this the following steps can be used :
we multiply the coefficients (3.4 and 2) and then add the exponents (2 and 3).
Multiplication of coefficients: 3.4 * 2 = 6.8
Addition of exponents: 2 + 3 = 5
Combining both parts: 6.8 x 10^5
The correct answer in scientific notation is therefore 6.8x10⁵, which corresponds with option B.
Matt had a full jar of marbles. He gave Kayla 3/4 of the marbles. Then Kayla returned 1/3 of a jar's worth of marbles to the jar. how much of the jar is full of marbles?
Answer: 7/12 jar is full of marbles
Step-by-step explanation:
Matt had full Jar of Marbles = 1
After giving 3/4 to Kayla , jar has marbles = [tex]1-\frac{3}{4} \\=\frac{4}{4} -\frac{3}{4} \\=\frac{1}{4}[/tex]
Kayla returned = 1/3 of Jar
Now jar has marbles = 1/3+ 1/4
= 4/12 + 3/12 [ making denominator same]
= 7/12
find the common ratio for this geometric sequence 8, 2, 1/2, 1/8, 1/32
Answer:
Multiply 1/4 ; dividing 4
Step-by-step explanation:
Note that in each number going from left to right, it decreases by dividing 4 each time (or multiplying 1/4)
8/4 = 2 ; 2/4 = 1/2 ; (1/2)/(4) = 1/8 ; etc.
(8)(1/4) = 2 ; (2)(1/4) = 1/2 ; etc.
~
Answer: 1/4
Step-by-step explanation:
When you own a pet, there are one-time costs, such as a leash, and continuing costs, such as food. Suppose the one-time costs for owning a small dog are $180, and the continuing costs are $400 per year Which function models the average annual cost of owning a small dog for x years?
Answer:
Average cost per year = 400 + 180/x
Step-by-step explanation:
Using the formula y=mx+b
We know that b is the y intercept or initial value. That would be the start up costs
m is the slope on costs each time x increases, that would be 400 per year
Costs = 400x + 180
To find the average cost per year, we need to divide by x
Average cost per year = (400x + 180)/x
= 400 + 180/x
Answer:
answer to this question is f(x) = (180 + 400x)/x
Describe and correct the error in rewriting the equation
2x - y=5
Y= -2x+5
2x - y = 5 subtract 2x from both sides
2x - 2x - y = 5 - 2x
- y = 5 - 2x
The sign "-" (minus) before y was lost.
Multiply: (3x + 7)(5x2 − 3x + 6)
Answer:
15x^3+26x^2-3x+42
Step-by-step explanation:
The multiplication is 15x³ +26x² - 3x + 42.
What is multiplication?Multiplication is the process of adding a number up to a given number.
The multiplication (3x + 7)(5x²-3x+6) is as shown:
(3x + 7)(5x²-3x+6)
= 15x³ - 9x² + 18x +35x²- 21x +42
= 15x³ +26x² - 3x + 42
Hence, the multiplication is 15x³ +26x² - 3x + 42.
To learn more about multiplication, click here:
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HELPP plzzzzz plzzzz
Answer:
121/100
Hope it helps!
Please help
Evaluate - 8×|12|
Answer:
-96 or 96
Step-by-step explanation:
this is because the distance from zero is twelve, so it could be -12 or 12, plug both into the problem and then solve.
the absolute value |x| of a real number x is the non-negative value of x without regard to its sign.
|x| = x for x ≥ 0.
|x| = -x for x < 0.
Examples:
|2| = 2
|-5| = -(-5) = 5
If is -8 × |12| = -8 × 12 = -96
If is 8 × |12| = 8 × 12 = 96
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long? Be sure to show your work using the equation above.
Answer:
17.922
Step-by-step explanation:
first you plug it in
y=0.860(17) + 3.302
then u simplify
y=14.62+3.302
then add them
y=17.922
Answer:
17.922 inches long
Step-by-step explanation:
y=0.860x + 3.302
y= 0.860(17) + 3.302
y= 14.62 + 3.302
y= 17.922
Hope it helps!!
is Y=2 to the 2nd power linear or non linear why?
Answer:
Linear
Step-by-step explanation:
y = 2^2
y = 4
This is a line. 4 is constant.
Y to a constant value is a horizontal line
x-y<3
Do I need to flip the sign?
Rewrite in simplest radical form
Answer:
sqrt(x)
Step-by-step explanation:
1/ ( x^(-3/6))
We can simplify the fraction
1/ ( x^(-1/2))
A negative exponent means that since it is in the denominator, it goes to the numerator. It still keeps the exponent.
x^ (1/2)
sqrt(x)
The temperature today is 7 degrees celsius. Yesterday it was 13 degrees celsius cooler. What was the temperature yesterday?
Answer:
The temperature yesterday was -6 because 7-13 is -6.
Step-by-step explanation:
Answer:
The yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.
Step-by-step explanation:
The temperature today is 7 degrees Celsius. Yesterday was 13 degrees Celsius cooler. That the temperature is colder means that the temperature was lower than today's temperature. This means that to obtain the temperature on the previous day, 13°C must be subtracted from today's temperature.
yesterday’s temperature=today’s temperature-13°C
It is now possible to replace today's temperature with 7 ° C
yesterday’s temperature=7°C-13°C
Remember that to subtract two integers of a different sign (one positive and the other negative), as in this case, you must subtract their absolute values (that is, subtract 13-7 = 6), and the answer will have the same sign as the number with the highest absolute value (absolute value or module of any real number is the same number but with a positive sign). As in absolute value 13 is greater than 7, the answer to the subtraction will be negative
yesterday’s temperature=7°C-13°C
So, finally, the yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.